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Pocket reading list : Week 1.1 of July

On spaghetti sauce - Malcolm Gladwell : There's a lot to learn from how products are priced and the is a lot of science behind why the product lineup is what it is. Apparently, when companies approached a consultant to help them revive their product, conduct customer surveys and help defeating their rivals. What the consultant suggested was revolutionary, for the time. This is a story of what the consultant understood from his understanding of the human condition.

The Arctic Suicides: It's Not The Dark That Kills You : Urbanisation, in many parts of the world, is on full swing, and it's moving at an especially fast and frighteningly pace in some parts of the world! This account tells us what can go wrong if this urbanisation, and it's effect on the native population, isn't handled with care. It's surprising, shocking and sad that the deaths of so many natives isn't receiving a broader public attention.

Why the S.E.C. Didn’t Hit Goldman Sachs Harder : Goldman Sachs was one of the companies responsible for the recent financial crash, that the world is still recoiling from. And the S.E.C. (Securities and Exchanges Commission) of the U.S.A. was trying to indict people at the (investment) bank for having an active role in the crash. But at the end of the day, the fine they received would've been recuperated by the bank in less than a month. This account talks about internal forces that were trying to dial down the efforts of the S.E.C. and preventing it from targeting higher-ups in the chain of command at the bank.

The Really Big One : This is what a pulitzer prize winning piece looks like, I guess. For those of you who've watched the movie San Andreas, you might know that the state of California can be badly affected by an earthquake, an earthquake that is long due. In reality, science tells us that the San Andreas fault isn't really the one that we should be scrutinising. It's precise and a scary account of what the consequences of a big earthquake are, one bigger than what Japan experience in the recent Tsunami that led to the Fukushima disaster.

‘Where Is This Flight Going?’ and Other Basic Questions About African Travel : I started with a relatively light story and I'll end with one. This is an account of the air travel industry in Africa.

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In the image, you see 5 static curves and one dynam…

Pandas download statistics, PyPI and Google BigQuery - Daily downloads and downloads by latest version

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This was just a fun first query/question.
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Adaptive step size Runge-Kutta method

I am still trying to implement an adaptive step size RK routine. So far, I've been able to implement the step-halving method but not the RK-Fehlberg. I am not able to figure out how to increase the step size after reducing it initially.

To give some background on the topic, Runge-Kutta methods are used to solve ordinary differential equations, of any order. For example, in a first order differential equation, it uses the derivative of the function to predict what the function value at the next step should be. Euler's method is a rudimentary implementation of RK. Adaptive step size RK is changing the step size depending on how fastly or slowly the function is changing. If a function is rapidly rising or falling, it is in a region that we should sample carefully and therefore, we reduce the step size and if the rate of change of the function is small, we can increase the step size. I've been able to implement a way to reduce the step size depending on the rate of change of …